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Histograms with Equal Class Widths

FoundationHigherAQAEdexcel

Practise Histograms with Equal Class Widths for GCSE Statistics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA and Edexcel. Histograms display grouped continuous data using bars with no gaps between them.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA and Edexcel specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A histogram represents continuous data with bars that touch, because the class intervals are adjacent with no gaps.

When all the class widths are equal, the height of each bar is simply the frequency, and the histogram looks much like a bar chart. The essential difference is that there are no gaps between the bars.

The horizontal axis is a continuous number line rather than a set of categories, so the bars must be drawn at the correct positions and widths along it. Both axes must be labelled, and the frequency axis must start at zero. When class widths are unequal, frequency density must be used instead of frequency.

Revision notes

Equal class widths

When all class widths are equal, the bar height is simply the frequency.

The histogram then resembles a bar chart, but with no gaps between the bars because the intervals are adjacent along a continuous scale.

Histograms versus bar charts

Histograms are for continuous data; bar charts are for categorical or discrete data.

Histogram bars touch; bar chart bars have gaps. The horizontal axis of a histogram is a continuous number line, not a set of separate categories.

Drawing correctly

Both axes must be labelled and the frequency axis must start at zero.

Bars must be drawn at the correct positions along the horizontal scale, with widths matching their class intervals. When widths are unequal, frequency density must be used instead.

Key points

  • Histogram bars touch with no gaps.
  • Histograms represent continuous data.
  • Equal class widths mean height equals frequency.
  • The horizontal axis is a continuous scale.
  • Both axes must be labelled.
  • Unequal widths require frequency density.

Worked examples

Example 1

A histogram has equal class widths. The class \(20 \leq x < 30\) has frequency 14. State the height of that bar. [1 mark]

Working

14with equal class widths the height equals the frequency

Example 2

Explain why the bars of a histogram touch. [2 marks]

Working

The class intervals are adjacent along a continuous scale with no gaps between themstate the reason
so leaving gaps would suggest values exist for which there is no intervalexplain the consequence

Example 3

State two differences between a histogram and a bar chart. [2 marks]

Working

A histogram has no gaps between bars, whereas a bar chart doesgive the first difference
A histogram represents continuous data, whereas a bar chart represents categorical or discrete datagive the second difference

Common mistakes

  • Leaving gaps between histogram bars.

    The intervals are adjacent, so the bars must touch.

  • Using a histogram for categorical data.

    Histograms require continuous data.

  • Using frequency as the height when widths are unequal.

    Frequency density must be used in that case.

  • Not labelling the axes.

    Both must be labelled to earn full marks.

Exam tips

  • Check whether the class widths are equal before choosing the height.
  • Draw the bars touching.
  • Label both axes and start frequency at zero.
  • Learn the histogram versus bar chart differences.

Key terms

Histogram
A diagram for continuous data with touching bars.
Continuous data
Data that can take any value in a range.
Class width
The size of a class interval.
Frequency density
Frequency divided by class width, used for unequal widths.

Related topics

Written and reviewed against the current AQA and Edexcel specifications. Spotted an error? Let us know.